A new technique has been developed for the treatment of
hydrodynamic loss processes from planetary atmospheres
utilising the Godunov method. A detailed description of a
first order Godunov scheme is given by Godunov (1959),
Gombosi (1984), and Leveque (2002). Solving the
one-dimensional, steady state approximation becomes
problematic at the distance where the outflow becomes
supersonic. This method overcomes the instabilities inherent
in modeling transonic conditions by solving the coupled,
time dependent mass, momentum, and energy equations, instead
of integrating time independent equations. We validate a
preliminary model of hydrodynamic escape against simple,
idealised cases (viz., steady state and isothermal
conditions) showing that a robust solution obtains and then
compare to existing cases in the literature (Watson et al.,
1981; Kasting and Pollack, 1983; Chassefiere, 1996). A focus
of this work is on observable aspects of atmospheres that
may be useful for comparison between models and
observations. "Close-in" hot Jupiter's provide an ideal test
case because of recent observations of HD 209458b. The
general tools developed here will be applied to various
problems such as the early Earth and Venus, and close-in
extrasolar gas giant planets and are directly applicable to
modifications required for the VPL terrestrial planet
models.